Mem. S.A.It. Suppl. Vol. 26, 38 Memorie della c SAIt 2014 Supplementi The Hungaria Asteroids: close encounters and impacts with terrestrial planets M. A. Galiazzo, A. Bazso, and R. Dvorak Institute of Astronomy, University of Vienna, Turkenschanzstr.¨ 17, A-1180 Wien, Austria e-mail: [email protected] Abstract. The Hungaria asteroid family (Named after (434) Hungaria), which consists of more than 5000 members with semi-major axes between 1.78 and 2.03 AU and have in- clinations of the order of 20◦, is regarded as one source for Near-Earth Asteroids (NEAs). They are mainly perturbed by Jupiter and Mars, and are ejected because of mean motion and secular resonances with these planets and then become Mars-crossers; later they may even cross the orbits of Earth and Venus. We are interested to analyze the close encounters and possible impacts with these planets. For 200 selected objects which are on the edge of the group we integrated their orbits over 100 million years in a simplified model of the planetary system (Mars to Saturn) subject to only gravitational forces. We picked out a sam- ple of 11 objects (each with 50 clones) with large variations in semi-major axis and some of them achieve high inclinations and eccentricities in connection with mean motion and secular resonances which then leads to relatively high velocity impacts on Venus, Earth and Mars. We report all close encounters and impacts with the terrestrial planets and statistically determine the mean life and the orbital distribution of the NEAs of these Hungarias. Key words. Hungarias – asteroids – close encounters – impacts – NEAs – terrestrial plan- ets 1. Introduction In the first place this is deduced from the spec- tral type of the major component of the fam- The Hungaria group contains about 8000 as- 1 ily, the E-type or Achondritic Enstatite (about teroids, located in orbital element space be- 60%) , which is consistent with the composi- tween 1:78 < a(AU) < 2:03, e < 0:19 and ◦ ◦ tion of some meteorites (aubrites, Zellner et al. 12 < i < 31 , inside the ν6 secular reso- (1977) found on the Earth. Other Hungarias are nance (SR) and the mean motion resonances also S-type (17.2%) and less C-types (6.0%) (MMRs) 4:1 with Jupiter (J4:1) and 3:4 with (Warner et al. 2009). The objects of the group Mars (M3:4). are not very big in size compared to the other There is evidence from meteorites that Main Belt Asteroids (MBAs), they have an av- members of the Hungaria group may reach the erage diameter of 1 km ranging up to 11.4 km, terrestrial planets and be a source of impactors. (434)Hungaria being the biggest member. The 1 majority of Hungarias have a retrograde rota- following in part a suggestion of Spratt (1990), tion and similar spin rates (Pravec et al. 2008; so that our sample finally consisted of 8258 aster- Rossi et al. 2009). oids (August 2010) Galiazzo: The Hungaria Asteroids 39 The content of the paper is as follows: considered a close encounter when the aster- oid crosses the following distances (close en- – methods and details on the investigated counter radius, CER) from each planet: the av- bodies; erage lunar distance 0.0025 AU for the Earth, – statistical and analytical study on and the lunar distances scaled to the respec- Hungarias path to be NEAs, impacts tive Hill Sphere of the other 2 considered plan- and close encounters with the Terrestrial ets 0.00166 AU for Mars and 0.00170 AU for planets; Venus. – conclusions: discussion and summary on the previous described studies. 3. Results 3.1. Statistical analysis of the dynamics 2. Methods and details of the Hungarias’ Fugitives. Hungaria asteroids was picked up from The 11 fugitives are also inside the Hungaria the database2 of the Lowell observatory at Family, so it is possible to speak about escapers Flagstaff, then a reasonable number of aster- from the family, a more restrictive definition of oids was taken for the orbital integrations: 200 “group”; we remember here the definitions: out of the total Hungarias inside the group, the ones that have the higher deflection from the Group: a “group” of asteroids is defined by average of a metric d based on the osculating a range of osculating elements (see also q elements: d = ( e )2 + ( a )2 + ( sin i )2 Warner et al. 2009) <e> <a> <sin i> Family: a (dynamical) “family” of asteroids (a, e and i are respectively the semi-major axis, is defined by the use of the proper ele- the eccentricity and the inclination of the aster- ments. Families are defined by a specifi- oids). cal clustering method, which gives dynam- Firstly these first sample was integrated for ically a homogeneous sample of asteroid 100 My with the Lie-integrator (Hanslmeier in the Main Belt, the most well known are & Dvorak 1984; Eggl & Dvorak 2010) the Hierarchical Clustering Method (HCM, in a simplified Solar system (planets from Zappala´ et al. 1990) and the Wavelet 3 Mars to Saturn), enough for the scope of this Analysis Method (WAM, Bendjoya et al. first work, discovering the objects which es- 1991). cape from the group: 11 bodies (see Table 1). They were discriminated considering only The orbit of the fugitives is rather chaotic those ones who has a major deflection in the after a close encounter as it can be seen in the semi-major axis: ∆a > ∆agroup=16 = 0:01563 case of (41577) 2000 SV2 (Fig. 2). This as- AU, with ∆a = amax − amin: deviations from teroid become a Sungrazers in less than 100 the group’s mean semi-major axis of more than Myrs, crossing the ν6 secular resonance at ∼ ∼ 7% of the total width of the group. 71Myr and then after a very close encounter Secondly the 11 fugitives were integrated with Venus, it become a NEAs keeping a high again with the same initial conditions and to- value of eccentricity, always e > 0:3, finally gether with 49 clones for each one of them in- after several close encounters with all the plan- side these ranges: a ± 0:005 AU, e ± 0:003 and ets, it collides the Sun. i ± 0:005◦. This time in a Solar System which During the orbital evolution of 100 Myrs, take in accounts all the planets from Venus to all the Fugitives become Mars-crossers. 91 % Saturn, so taking in account also the terres- of them (the clones) are planet crossing as- trial planets and all the close encounters. It is teroids (PCAs) and 58% NEAs, in particu- lar Amors and Apollos: Amors are the Earth- 2 www2.lowell.edu/elgb approaching NEAs with orbits exterior to the 3 Integrations with the full Solar System from Earth’s (a > 1:0AU and 1:017(AU) < q < Mercury to Neptune shows the same general results. 1:3(AU); Apollos are Earth-crossing NEAs 40 Galiazzo: The Hungaria Asteroids Fig. 1. The Hungaria group in the orbital space and the metric. Reddish crosses are for the asteroids with the most extreme value in the metric. with semi-major axis larger than the Earth (a > ing them. In order to make this the diameter 1:0 AU and q < 1:017 AU, q is the perihelium), of the asteroids is needed, see (Table 1). They this means that 3.2% of all the Hungarias be- are computed with the equation of Fowler & come NEAs in 100 Myrs. The average time- Chillemi (1992), which gives a quite precise evolution of the Hungarias escapers is shown results, with an error, usually of second order in Fig. 3, a Fugitive usually have a close en- (if the diameter is 220km the error is about of counter with Earth and Venus after becoming 201km, see Galiazzo 2009): D = 1329p 10−H=5. ρv an Amor, an Apollo and an Aten. The entry velocity at the CER for each The estimates of the diameter of the planet it is 21:5 ± 2:3 km/s for the Earth, Hungaria-impactors are based on the assump- 27:8 ± 1:7 km/s for Venus and 10:8 ± 1:0 km/s tion that the asteroid has a spherical shape. for Mars. The known impact structures on Earth range from small circular bowls only a few 3.2. Impacts hundred metres in diameter to large com- plex structures more than 200 km in diameter Some singular clones have an impact with a (French 1998), with ages as old as 2 Gyr. The terrestrial planet. The percentage of the whole biggest known craters on Earth are Vredefort Hungaria’s population having an impact with a and Sudbury craters, larger than 200 km in di- terrestrial planet during 100 Myrs is: 0.7% for ameter. The “projectiles” capable of forming the Earth, 2.4% for Venus and 1.1% for Mars. craters on the terrestrial planets today come It is possible to compute the diameter of the pu- primarily from three populations(Ivanov et al. tative craters and some typical values concern- 2002a): Galiazzo: The Hungaria Asteroids 41 Fig. 2. Upper panel: semi-major axis and Planetocentric distance versus time. In blue, green and red, close encounters with respectively: Mars, Venus and Earth. Bottom panel: eccentricity (red), inclination (black) and perihelium (blue) versus time. Fig. 3. Average time-evolution of a Fugitive. Each “x” represents 1 Myr. Atens are Earthcrossing NEAs with semimajor axis smaller than the Earth: a < 1:0 AU and Q > 0:983AU (Q is the aphelion); Atiras have the orbit contained with the one of the Earth: a < 1:0 AU and Q < 0:983 AU.